Unformatted text preview: BUSI 403 Problem Set C Fall 2008 Due: 09/11/08 Problem 1 a. Determine the Economic Order Quantity, the time between placement of orders and the total annual cost (i.e., sum of holding and ordering costs) incurred by KCC EOQ = = A D
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H C C = 200 Thus, the EOQ is Q* = 200 The time between order placements = EOQ / Annual Demand = 200 / (12*600) = 0.0278 year = 1/3 month Annual Holding Cost = (Q* /2) * Unit Holding Cost = (200/2) * (0.15 * 720) = 10,800 Annual Ordering Cost = (Annual Demand / Q* )*Ordering Cost = (12 * 600)/200 * 300 = 10,800 Total Annual Cost = Annual Holding Cost + Annual Ordering Cost =$21,600 b. If the order lead time is 4 days and KCC operates 25 days each month, what is the reorder point based on the level of on‐hand inventory? Daily demand rate = 600/25 = 24 tons/day Reorder point = Daily demand rate * lead time = 24 tons/day * 4 days = 96 tons c. Suppose the supplier requires orders to be placed in multiples of 300 tons. How much additional total annual cost would KCC incur to meet this requirement? From part a we know that the EOQ is Q* =200 < 300. Therefore instead of ordering 200 tons, KCC has to order Q = 300 tons every time. In that case, we have Annual Holding Cost = (Q /2) * Cost of Holding = (300/2) * (0.15 * $720) = $16,200 Annual Ordering Cost = (Annual Demand / Q )*Order Cost = (12 * 600)/300 * $300 = $7,200 Total Annual Cost = Annual Holding Cost + Annual Ordering Cost =23,400 From part a we know that the total annual cost with EOQ is 21,600. Therefore KCC incurs $23,400 – $21,600 = $1,800 in addition annually. 1 BUSI 403 Problem Set C Fall 2008 Due: 09/11/08 Problem 2 a. What is the safety stock for the battery if Toyota wants to maintain a service level of 95%? For a 95% service level, the z value is 1.645. (Using the Excel function NORMINV(0.95,0,1) = 1.645) Safety stock = z * standard deviation of monthly demand * lead time = 1.645 * 230* √1 review period 1 = 535 b. What is the annual holding cost for this safety stock? Annual Unit Holding Cost = $100 /month per unit* 12 month/year = $1200 /year per unit Annual Holding Cost for Safety Stock = $1200 / year per unit * 535 unit = $642000 c. What is the average inventory on order/ in transit? In‐transit inventory = mean demand * (lead time + review period) = 2000 * (1 + 1) = 4000 d. How much additional safety stock does Toyota have to carry to reach a service level of 98%? For a 98% service level, the z value is 2.053. (Using the Excel function NORMINV(0.95,0,1) = 2.053) Safety stock = z * standard deviation of monthly demand * lead time review period = 2.053 * 230 * √1 1 = 668 Recall from part (a) that the safety stock with 95% service level is 535. Therefore additional safety stock = 668 – 535 = 133. 2 BUSI 403 Problem Set C Fall 2008 Due: 09/11/08 Problem 3 a. Perform an ABC classification. Make sure that 20% of the SKUs are classified as A, and not less than 50% of items are classified as C (with the remaining classified as B). Monthly Demand (tons) Unit Cost Monthly Sales Cumulative Monthly Sales Cumulative Percentage Category 864900 23.79% A 833625 1698525 46.71% A 810 704700 2403225 66.09% A 750 730 547500 2950725 81.15% B BE‐223 641 400 256400 3207125 88.20% B 6 CR‐315 642 320 205440 3412565 93.85% B 7 GN‐381 212 210 44520 3457085 95.07% B 8 HR‐152 166 200 33200 3490285 95.99% C 9 CS‐471 122 270 32940 3523225 96.89% C 10 AS‐218 142 190 26980 3550205 97.63% C 11 SS‐183 259 90 23310 3573515 98.27% C 12 CR‐712 218 100 21800 3595315 98.87% C 13 BE‐125 88 220 19360 3614675 99.41% C 14 BE‐135 120 120 14400 3629075 99.80% C 15 CR‐167 144 50 7200 3636275 100.00% C Product Number 1 BE‐142 961 900 864900 2 BE‐225 975 855 3 TU‐522 870 4 TU‐131 5 Note that other partitions could also be possible. This partition is formed by considering 50% of the items as category C. b. Based on your classification in part a, what percentage of the total monthly sales is in each category A, B and C? Using the classification in part a), 66.09% of sales value is classified as category A, (95.07–66.09) = 28.98% of sales value is classified as category B, (100‐95.07) = 4.93% of sales value is classified as category C. 3 ...
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